Difficult questions all...
Shortage of small coins is caused by the coin becoming obsolete as its value is too low. However, it will be obsolete to rich people before becoming worthless to poor people and there's the crux. The US cent is clearly obsolete, as it is easy to find them on the sidewalks, in the post offices and stations of NY.Is it also obsolete in the small villages of Mississippi or Alabama? Maybe. However, even though some states of the US qualify as developing countries, the US is a rich country in its totality, therefore the US solution is to strike millions of cents. These cents don't circulate much, as rich people will refuse them, throw them away or pile them up somewhere, but they may be used in the poorest parts of the US. In this way, the rich are helping the poor in a very small way.
Though India also has rich and poor areas, it is a poor country in its totality, so the US solution is not feasible. India's solution is apparently to strike insufficient quantities and wait if there's an outcry. If there is, they assign more coins to that region. Where there's no outcry, supply is choked off.
There is a similar situation in te EU, which has poor as well as rich countries, but since member states can decide themselves which coins to issue or not, the problem is mitigated. The EU solution is not to care if member states do or don't want the 1 and 2 cent pieces. Finland rounds prices, in the Netherlands you are allowed, but not obliged to round, others don't. Germans don't like the small change, but the Greeks need them and so will some new entrants.
Where I see cash disappear is rather on the high value side. The poorer member states insisted on the largest notes, while in the richer ones, large notes are often refused. As the payment system develops (personal checks in France, debit cards in most other countries) you need large value notes less and less.
Interestingly, systems for small payments fail. PayPal does work, but in a niche of the US market. It's way too expensive (4%!) for anything except forced use on eBay. Probably, you'll see banknotes disappear before coins.
Peter